Climate change-driven ocean warming is increasing the frequency and severity of bleaching events, in which corals appear whitened after losing their dinoflagellate endosymbionts (family Symbiodiniaceae). Viral infections of Symbiodiniaceae may contribute to some bleaching signs, but little empirical evidence exists to support this hypothesis. We present the first temporal analysis of a lineage of Symbiodiniaceae-infecting positive-sense single-stranded RNA viruses (“dinoRNAVs”) in coral colonies, which were exposed to a 5-day heat treatment (+2.1 °C). A total of 124 dinoRNAV major capsid protein gene “aminotypes” (unique amino acid sequences) were detected from five colonies of two closely related Pocillopora-Cladocopium (coral-symbiont) combinations in the experiment; most dinoRNAV aminotypes were shared between the two coral-symbiont combinations (64%) and among multiple colonies (82%). Throughout the experiment, seventeen dinoRNAV aminotypes were found only in heat-treated fragments, and 22 aminotypes were detected at higher relative abundances in heat-treated fragments. DinoRNAVs in fragments of some colonies exhibited higher alpha diversity and dispersion under heat stress. Together, these findings provide the first empirical evidence that exposure to high temperatures triggers some dinoRNAVs to switch from a persistent to a productive infection mode within heat-stressed corals. Over extended time frames, we hypothesize that cumulative dinoRNAV production in the Pocillopora-Cladocopium system could affect colony symbiotic status, for example, by decreasing Symbiodiniaceae densities within corals. This study sets the stage for reef-scale investigations of dinoRNAV dynamics during bleaching events.